Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x + 7$ and $ KL = 8x - 20$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x + 7} = {8x - 20}$ Solve for $x$ $ -3x = -27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({9}) + 7$ $ KL = 8({9}) - 20$ $ JK = 45 + 7$ $ KL = 72 - 20$ $ JK = 52$ $ KL = 52$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {52} + {52}$ $ JL = 104$